Magnitude of Electric Field at a Point

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SUMMARY

The magnitude of the electric field at a point inside a uniformly charged sphere is zero, as established by Gauss's Law. This conclusion is supported by the MIT lecture referenced, which indicates that for a conducting spherical shell, the electric field inside is null due to symmetry. However, the discussion also references a nonzero equation (kQr/R^3) from 'Physics for Scientists and Engineers' by Serway/Jewett, which applies to a solid non-conducting sphere where the electric field varies with distance from the center. The key distinction lies in the type of sphere being analyzed: conducting versus non-conducting.

PREREQUISITES
  • Understanding of Gauss's Law
  • Familiarity with electric field concepts
  • Knowledge of charge distribution in conductors and insulators
  • Basic calculus for understanding electric field equations
NEXT STEPS
  • Study Gauss's Law applications in electrostatics
  • Learn about electric fields in non-conducting materials
  • Explore the differences between conducting and non-conducting spheres
  • Review example problems in 'Physics for Scientists and Engineers' by Serway/Jewett
USEFUL FOR

Students preparing for physics exams, educators teaching electrostatics, and anyone interested in the principles of electric fields and charge distributions.

tylerc1991
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Homework Statement



Given a sphere of radius R with a uniform charge distribution Q, what is the magnitude of the electric field at a point p0 inside of the circle?

Homework Equations



Flux = 4 pi r^2 E = Q/epsilon

The Attempt at a Solution



So I was watching an MIT lecture online (youtube is great for that), and the professor was doing this problem. When finding the magnitude of the electric field at a point inside of the sphere, he found it to be zero, which made perfect sense to me. Now studying for a test and reading through the book, I find this exact same problem, only now the magnitude of the electric field is given by a nonzero equation (kQr/R^3, where r is the distance from the center of the sphere to the point and r < R). (If anyone happens to have the book its 'Physics for Scientists and Engineers' vol 8 by Serway/Jewett, and the example is 24.3). So my question is this: who is correct? Is the magnitude of the electric field in fact 0 or is it related by the equation above?
 
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In one case you have a conducting spherical shell with a given charge Q, evenly distributed over its surface. In your case you have a "solid" nonconducting sphere with charge Q distributed throughout.

Draw a Gaussian surface with some radius inside the sphere. What's the total charge contained therein?
 

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